# Electron spin resonance

With the aid of electron spin resonance (short ESR or English electron paramagnetic resonance , EPR ), the resonant microwave absorption of a sample in an external magnetic field measured. This makes it an excellent method for examining samples that have a permanent magnetic moment (unpaired electrons ).

## history

The first ESR experiment was carried out by Yevgeny Konstantinowitsch Sawoiski in Kazan in 1944. Independently of this, the development in Great Britain was carried out by Brebis Bleaney . In paramagnetic salts such as copper sulfate and manganese (II) chloride, Sawoiski observed resonance absorption of the radiated energy at defined ratios of the strength of the static magnetic field to the frequency .

## background

If you bring a sample with a permanent magnetic moment into a magnetic field, the degenerate energy states split up ( Zeeman effect ). Often the Zeeman effect is investigated on the basis of transitions between levels of different principal quantum numbers ; With ESR, on the other hand, transitions between levels of the same principal quantum number are observed: By irradiation with a microwave , the energy of which corresponds to the splitting of the levels, absorption occurs.

In practice, the sample to be examined is irradiated in a variable magnetic field with a fixed frequency microwave. The recorded absorption spectrum allows conclusions to be drawn about the magnetic environment of the magnetic moments (see g-factor ).

In ESR spectroscopy, only substances with one or more unpaired electrons can be examined. Typical examples are:

## application

ESR spectroscopy is used, for example, in biophysics and in semiconductor physics . ESR can be performed on natural biological samples. Diseased tissue can thus be examined and statements about irradiated material can be made using the radical concentration.

ESR is also an investigation method in materials research . In photovoltaics, for example, contamination of the material can be limited by characterizing paramagnetic defects.

For the structure elucidation of macromolecules , such as proteins , lipids , DNA or RNA , is suitable ESR when couples the macromolecules previously with spin labels. As a spin marker proteins are nitroxides used, an unpaired, via the NO bond delocalized contain electron and a bond with cysteine in an amino acid sequence received. Distances between two bound spin markers can be determined from the ESR spectra and thus conclusions on z. B. pull the folding of protein strands. An established procedure for this is the double electron electron resonance (DEER), a pulsed variant of the ESR, in which non-overlapping pulses are emitted at different frequencies. The method is also suitable for investigations into protein-membrane interactions.

The narrow-band electron spin resonance of monocrystalline yttrium iron garnet in a magnetic field is used to manufacture microwave filters ( YIG filters ) and resonators.

## Resonance absorption

A static (mostly homogeneous ) magnetic field in which there are atoms or molecules with non-closed electronic shells cancels the energetic degeneration of the states ( Zeeman effect ). As a first approximation, this split is proportional to the applied magnetic field : ${\ displaystyle H}$

{\ displaystyle {\ begin {alignedat} {2} E _ {\ rm {Zee}} & = g \ cdot \ mu _ {0} && \ cdot \ mu _ {\ mathrm {B}} \ cdot m_ {J} \ cdot H \\ & = g && \ cdot \ mu _ {\ mathrm {B}} \ cdot m_ {J} \ cdot B \ end {alignedat}}}

With

• the Bohr magneton ${\ displaystyle \ mu _ {\ mathrm {B}}}$
• the magnetic flux density ${\ displaystyle B = \ mu _ {0} \, H}$
• the magnetic quantum number .${\ displaystyle m_ {J}}$

Each magnetic energy level therefore has the distance from the next neighboring state (equidistant splitting). Magnetic dipolar transitions between neighboring levels are possible between the states ( ). ${\ displaystyle E_ {0} = g \ cdot \ mu _ {0} \ cdot \ mu _ {\ mathrm {B}} \ cdot H}$${\ displaystyle \ Delta m_ {J} = \ pm 1}$

If a high-frequency alternating field is applied perpendicular to the static magnetic field (e.g. with X-band ESR 9 to 10  GHz ), these transitions can be specifically stimulated. To do this, the magnetic energy must correspond to the microwave energy . In this case, microwave radiation of the frequency is emitted or absorbed - resonance absorption is observed. ${\ displaystyle E_ {0}}$${\ displaystyle h \, f}$${\ displaystyle f}$

In the case of paramagnetic resonance, this results in the resonance condition (also called "basic equation of EPR spectroscopy"):

${\ displaystyle g \ cdot \ mu _ {0} \ cdot \ mu _ {\ mathrm {B}} \ cdot H = h \ cdot f}$

The g-factor (or Landé factor) links the magnitude of the magnetic moment of an atom with its total angular momentum :

• for pure orbital magnetism (i.e. spin )${\ displaystyle s = 0}$${\ displaystyle g = 1}$
• for pure spin magnetism (i.e. orbital angular momentum ) applies (more precisely 2.002322).${\ displaystyle l = 0}$${\ displaystyle g = 2}$

In general, the following relationship can be specified:

${\ displaystyle g = 1 + {\ frac {j (j + 1) + s (s + 1) -l (l + 1)} {2j (j + 1)}}}$.

This formula can be derived from the vector model of atomic physics .